There is no interference with single photons of light, there is only hokuspokus. Feynman shows (and he brought many to the way of physics) that he is able to create a math based model that explains why light does, what it does, but that is all. He explains light to us, the unlighted, but not to the light itself.
There is no interference with single photons of light, there is only hokuspokus.
Well, it all sounds like hokuspokus but for about a hundred years now experimental results demonstrate that something weird is going on.
On the one hand we have experiments that demonstrate the photon nature of light. You can count them one by one as you might expect for some kind of indivisible particle.
On the other hand, even if you are working with one photon at a time the place where it ends up, statistically after many experiments, is described by the notion of waves.
How can one particle-like thing explore the space of all options like a wave and end up where it does in a particle like manner?
I urge you to do the experiments.
Now, I do agree with you. Perhaps our notion of particles is wrong. Perhaps our notion of waves is wrong. Perhaps the mathematical models built from these notions is wrong.
When I say "wrong" I don't mean the mathematical models don't work to some extent but rather they are not capturing some essence of what is going on underneath.
That is what physics is all about, perfecting the notions, and hence the mathematical models.
Newton is famous for giving us his laws of gravitation. He also said "I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses". That is to say, the maths works but I have no idea why.
Feynman has said much the same.
Bottom line is, it's easy to poke fun at physics, but it's hard to come up with some useful ideas that work better.
Before I stood on a shore watching waves the first time, before I just saw them, I also felt puzzeled. But now I'm clear. That means not I have no problems, but I have them in another place.
Dualism is at large a method to show people that you are smarter. Since ever there is a discussion about atoms and continua. The perspective changed over the millenia. Now we know, yes, there is a continuum, but this continuum can be separated into local areas, which then are particles. But that doesn't mean, that there is a wave or a particle, it just means that there is a way to have located standing waves. Whatever a standing wave looks like. A wave caught between two mirrors is a very simple example. A wave caught in the atom is much more complicated, but follows the same concept.
By the way: Feynman wrote a lot, as every scientist writes a lot over his lifetime, only a few is narrated. Feynman showed: if we have a wave and in the running path of this wave are gratings, then the interference pattern of the wave encodes the structure of the grating. And he showed, that when the grating is of infinity density, then the interference pattern is that of a free running wave. Therefor he said: let us asume, the free space is an grating such dense, that we can not proof the existence. But now we can calculate the movement of wavelets and calculate all the possible pathes and in the end we see that the shortes path is nothing but the interference of all thinkable pathes. This is just a mathematical approach. Now, that you have this dense grating you can introduce disturbances and calculate what happens now. The same mechanism works if you try to understand semiconductors and doping
I think it is fair to ask... when is momentum=Planck'sConstant_h/wavelength? Is it true over time, instantaneously or both?
It makes a certain amount of sense that if one has two oscillator operating at two different frequencies with the same quantum efficiency, then during a certain period, the number of photons is going to be proportional to the frequency... giving a rational explanation for this relation.
But if I understand what Erna is saying(and which I have believed for a while might actually be the case): In the case of single photons... (the instantaneous case) the momentum of all photons is the same and therefore a quantum of action is defined and can be assigned a value of 1.
Actual values of Pi must be discreet. There is no need for a number which cannot be expressed.
...when is momentum=Planck'sConstant_h/wavelength?
In classical, Newtonian, physics an object, say an electron, billiard ball or planet, has a momentum p = m * v. Where m is it's mass and v it's velocity. It also has energy E = m * v * v / 2.
Both these quantities are conserved. So two colliding objects may have different energies after they collide than they had before but the sum of their energies is the same. Similarly for the sum of their momenta.
So what about light?
We observe that light comes in lumps. We can see this by playing with photo-multiplier tubes, basically the photo-electric effect described by Einstein. These lumps of light, photons, carry energy. Obviously, else the sun would not warm us and photo cells would not work. They also, less obvious perhaps, carry momentum.
Energy E = h * f and momentum p = h / λ.
In short, the "when is momentum..." true when we have a photon in flight. Which is pretty much whenever we have a photon at all.
What about that conservation?
Hmm... Crash particles together and they may break up or combine to give different particles and photons flying out as wreckage. All those resulting bits will have the same total energy and momenta as the original particles. To account for that we use the above formulae.
It makes a certain amount of sense that if one has two oscillator operating at two different frequencies with the same quantum efficiency, then during a certain period, the number of photons is going to be proportional to the frequency... giving a rational explanation for this relation.
I can't make out what that is trying to say. Consider a laser, that is a resonant cavity, an oscillator. The number of photons it puts out can be increased by driving it harder, turn up the current, you get more photons hence energy out. But they all have the same frequency and each has carries the same energy.
But if I understand what Erna is saying(and which I have believed for a while might actually be the case): In the case of single photons... (the instantaneous case) the momentum of all photons is the same and therefore a quantum of action is defined and can be assigned a value of 1.
I can't make out what that is tryinng to say either. The momentum of a photon depends on it's wavelength, see above, they are not all the same. Unless you are talking of all photons of the same frequency.
Sure we could define Planck'c constant as 1. We would then have to redefine all our other units, length, time, etc to match. I'm not sure what advantage that has.
Now, where all this gets confusing is when we observe in experiment that we can get interference effects with particles like electrons, protons, even entire atoms and molecules. These interference effects look much the same as we see for light or sound or ripples in water. We can describe them using the mathematics of waves. So we are forced to the conclusion that particles have a wave like nature.
This recent experiment observes wave interference patterns created by streaming Bucky Balls (C60) though a diffraction grating. https://www.univie.ac.at/qfp/research/matterwave/c60/ I mean wow! A Bucky Ball is a huge molecule made of 60 carbon atoms. And there it is moving according quantum mechanical wave equations.
Actual values of Pi must be discreet. There is no need for a number which cannot be expressed.
I'm not sure what you mean by "discreet" here. There is only one actual value of Pi. It's the ratio of a circles circumference to it's diameter. Sure we use approximations.
Not sure what you mean by "cannot be expressed" either. Sure we cannot write down the exact numerical value but it is expressed as C/D. We use numbers that "cannot be expressed" all the time, e, i, the square root of two etc.
There is no interference with single photons of light, there is only hokuspokus.
Oh, but there is (not the hokuspokus, but the interference). The experiment is very simple. Dual slits, photographic film behind the slits, send a single photon at the time at the slits. After some time there will still be an interference pattern on the film, just as when you send a bunch of photons at the same time. That is very, very, very difficult to explain unless you accept that the single photons keep going through both slits.
I just ripped a shaft encoder wheel out of an old Cannon printer. If I squint really hard at it under good light I can just about make out the black stripes printed on the transparent wheel. I have no idea how many stripes per revolution that is.
Anyway, shining a red laser pointer through those stripes gives me a nice diffraction pattern on the wall. Which kind of surprises me as I thought we needed a much finer grating to do that. I have not done the maths on this yet.
Next step would be to turn the brightness down until we can count one photon at a time with a photo-multiplier tube or solid state photon counter. Scanning the image plane with the photon counter we should be able to plot the diffraction pattern.
I'd really like to do this because having read about it a lot and done the diffraction thing with lasers and x-rays I have never actually done the one photon at a time thing.
Where it gets weird of course is that this diffraction phenomena happens even with things we would normally say are solid particles, like electrons or whole molecules, that we would normally say cannot pass through many parts of a diffraction grating at the same time. But if one particle only passes through one slot in the grating how can there be an interference pattern?
Now one might say there are no particles only waves. But that leaves a lot of things unexplainable. Or say there are no waves only particles, again a lot of things, like interference, are unexplainable.
Or one might say we are just looking at it wrong, there is no particle and no wave, it's something else. Fine, what is the idea? Shows us the maths?
Why I use the term hokuspokus? Because a magician tries to meet your expectation and if you expect something wierds, you will take this for true. "hokuspokus" == "Hocus pocus" == hoc est enim corpus meum. You do not hear, what is said, but what you expect. So the single photon is a phantom, born from the ideas, that light might be a convolut of particles. But if you realize that under room temperature condition a square meter radiates 300W (?) of electromagnetic power, how we can create a single photon.
The idea of radiation consists of photon is not needed to understand the dualism of light waves: whenever a photon is absorbed, there is matter in play. And if matter can change state only in quanta, it is clear, that you will only see light quantums. But it is not the light, that is quantized, it's your measuring instrument that takes a quantum of energy from the field and stores it in a place.
How to understand the double slit experiment? Your target consists of molecules that when absorbing energy from the field, are "blackend". If now the field, that fills the vacuum, is carrying very low levels of waves of a given frequency, then the wave travelling through the slits interferes "constructively" and in the plane of the detector molecule by accident the constructed wave amplitude is sufficient to excite a molecule. A quantum of energy at the resonance frequency of the molecule is transfered from the field to the matter. That is what you call a photon.
That is: a photon is not a particle, light is made of, but it is the event of transfer from energy and momentum between field and matter. More we can not know, because we can not see the field itself, only interaction. That is why I say: hocus pocus. We need no quantized radiation to understand why energy exists in quanta.
Planck for example was very explicit in this. He said: in the walls of a hollow block body are oscillators and they quantize radiation. And he said: the spectrum we measure is independent of the frequency of the oscillators, if only the fundamental energy is low.
Einstein/Bose found: it is not the wall, that carrying the hypothetical oscillators, it is the space itself! If the walls are mirroring the radiation, that standing waves have a fundamental frequency and all harmonics. And if statistics is applied to calculate the ensembles of possible energy distributions, then the result is the black body radiation.
So the math doesn't change. It is only: there is a wave field, quantized by measuring it.
But to me there are other open questions: We know the term wave resistance, that is an "imaginated" resistance when a free wave exists and electric and magnetic field strength are related. (we also imagine a resistance, if we measure current and voltage, no need to understand the "mechanics" of the resistor.) So: when the big bang happend, and radiation started to travel away, is there a wave resistance where no wave ever travelled? We know, that a travelling wave, when arriving at different wave resistance is partly reflected. So if there is no wave resistance when there is no wave, will the wave front be partly reflected and so the expansion slow down?
That shows: if we overcome the hocus pocus, a lot of questions worth to discuss remain.
Hmm.. if I understand what you are saying about the vacuum field, and how it carries waves, then you are at best inventing new physics, or at worst back to the Aether and contradicting modern physics. But I'm not a physicist, so I'll not follow up on this anymore. But I can truly say that to me the simplest explanation is that the photon passes through both slits, it sounds much simpler than what you explain. I don't actually have much of an intuitive problem with that either, much as the intuitive problem I originally had with special relativity simply went away the more I learned about it. Now it *is* intuitive.
Why I use the term hokuspokus? Because a magician tries to meet your expectation and if you expect something wierds, you will take this for true.
True, we should always be careful of preconceived notions, intuition and the tricks of magicians. But my experience in this matter is that I was not expecting such weirdness when I started out my undergraduate physics. And I, like most kids in that position, rebelled against the quantum mechanical ideas, trying to dream up explanations for the experimental phenomena that made sense to our intuitive, classical minds.
It's like the time when I was 9 years old that my father happen to mention that nothing can travel faster than the speed of light. That made no sense to me. That's just a speed like any other, you can always go faster. My father was obviously wrong. Took a long while to start to understand why his statement had to be true.
Anyway, down to business:
So the single photon is a phantom...The idea of radiation consists of photon is not needed to understand the dualism of light waves:
So riddle me this:
1) I have a transmitter of light. Say a hydrogen atom with an electron in an excited state ready to drop down and emit light.
2) I have two receivers of light. Say photographic plates that register black dots when exposed.
3) I put my receivers far away from the transmitter in opposite directions.
4) My transmitter launches some light. That excited electron gives up it's "quanta" of energy.
5) That light travels in all directions, as you claim it's a wave, that's what a wave does. Therefore half the energy of our quanta goes towards one detector and half in the opposite direction to the other.
6) Now there is not enough energy going in either direction to register on any detector, There isn't enough to make up the "quanta" the detector requires.
7) Therefore my light energy can never be detected. It's floating around in space forever. Lost.
8 ) But it is! Either to one side or the other.
Are we to assume the emitted wave travels all the way to both detectors, say A and B, then somehow a decision is made that the "quanta" of of energy should be absorbed by one of them, say A? Which implies that the half of the energy that travelled to B now has to instantly move to A to complete the process. That can't be, it requires light to travel faster than light!
Or are we to assume that energy always stayed bound up in a particle like packet, a photon, that goes from emitter to detector in a lump. And causes the observed phenomena? That sounds more like it.
End of riddle.
Of course that photon lump of energy idea then presents a further puzzle. On the one hand our wave notions of light suggest that half of something went left to detector A and half went right to detector B. On the other hand our photon lump notion, that we are forced to accept by experiment as above, suggests the energy travelled in only one direction to A or B.
This brings us to the fundamental quantum mechanical wave/particle duality issue that has given me headache since 1976 and puzzled many far greater minds since a hundred years or so. Physicists still cannot agree among themselves on a single interpretation of all this.
If you think about it, the thought experiment above is equivalent to the slits experiment. Without the complication of interference.
Hmm.. if I understand what you are saying about the vacuum field, and how it carries waves, then you are at best inventing new physics, or at worst back to the Aether and contradicting modern physics. But I'm not a physicist, so I'll not follow up on this anymore. But I can truly say that to me the simplest explanation is that the photon passes through both slits, it sounds much simpler than what you explain. I don't actually have much of an intuitive problem with that either, much as the intuitive problem I originally had with special relativity simply went away the more I learned about it. Now it *is* intuitive.
The concept of Aether based on the concept of water and waves or gas and waves travelling. And then there is man, an observer. This observer is not a part of the Aether. From this concept result, that speeds add up linear, what is in contrast to observation, where speed of light is the speed limit. And constant. This moment the concept of Aether fails. But it could be the (unsaid) concept of an observer separated from the observed object, that failed.
Being a physicist or not: a single object being in two places in one moment is a contradiction in itself and that is the only reason, why a different solution must exist. Because this experiment exists and show the intereference and quantized behavior (particles).
But what is so strange in: if the propability of detecting a single photon is 1%, then 100 photons look like one? In this case, 50 photons can pass each slot and in this case the "detected" photon is the interference of both photon beams.
Heater: Imagine there is a background radiation, which is a mixture of all the frequencies with a given distribution. Following Plancks law. Planck already wrote: there is no base energy of which all the other energies are multiples, but whenever you assume a smallest quantum of energy, multiples are defined and then, when calculating how the available energy is distributed you will get the same spectral distribution. That means: if you could synthesize a black body radiation in a mirrored closed room by injecting photons, you could pull out photons of another base frequency so you will never see exactly the same frequencies, but the same spectrum.
This is a Gedankenexperiment, it can not be realized, because the concept of single photons is academic and to measure energy/wavelength you need more precision than the Heisenberg Uncertainty relation allows
When we do experiments with light, say the Young's slits experiment, we come to the conclusion that light is a wave phenomena. The mathematics of waves gives us the resulting interference patterns. Certainly Maxwell's equations deal with a wave phenomena and seem to fit the observations very well.
Other experiments, involving the photoelectric effect, or just doing that Young's slits experiment at very low light levels, lead us to the conclusion we are dealing with particles, aka photons. We can hear the single click of a photon counter, we can see the single dot exposed on a photographic plate.
The Young's slits experiment at very low light levels gives us a problem because now we observe both wave like and particle like behaviour in the same experiment. WTF?
It get's worse....
I can start with a lump of stuff. Say carbon. We can break it down to ever smaller and smaller parts. Ending up with C60 molecules for example, Bucky balls. At that point we have surely have "particles".
BUT, wait, we can now do the Young's slits experiment with a beam of those C60 particles and observe interference effects just like we see when we do the experiment with light "waves".
Holy cow, now we have to accept that our beam of solid particles is behaving like a beam of light waves.
Which of course is the stuff of Qunatum Mechanics.
All this leads me to the following conclusion:
If you insist that single photons do not exist then you are insisting that C60 molecules don't exist.
But what is so strange in: if the propability of detecting a single photon is 1%, then 100 photons look like one? In this case, 50 photons can pass each slot and in this case the "detected" photon is the interference of both photon beams.
Even if 100 photons looked like one for the receptor (film, or other photodetector), it wouldn't matter to the experiment because the originating photons were sent one at the time. That is, at different times. For those photons to create interference, without going two ways, would imply time travel. Well, that's also a possibility I suppose.. but I guess you won't like that one either.
Now, I assume that what you really mean is that we can't send one photon at a time. But we can, as is pretty clear for anyone learning electronics from scratch, at least late enough that semiconductors and transistors were on the curriculum. Transistors can't work unless quantum mechanics works exactly as described, and part of it is that if one electron drops from its shell to a lower shell, you get one (1) photon output. In any case, there are also real devices created for single photon output, so if you don't believe in single photons then you must also believe this device is a hoax: http://www.physique.ens-cachan.fr/old/franges_photon/single_photon_source.htm
And of course, the experiment has now been done with much bigger objects than photons, e.g. Heater's buckyballs.
You refer to how physical objects should behave according to intuition. But what is physical reality? Most of you, or as close to all of you as you can imagine, consists of nothing. When you press your hand on a table and feel resistance, what you feel is the force of electrons, it's not something physical, not really. Your weight, that is, the weight of your protons, are 92% or so due to relativistic effects (mass increases as speed increases) of the insane speeds of the quarks your protons are made of. What are electrons made of?
The problem with physical objects and reality is, I believe, that we don't actually understand, yet, what it is. And what we observe with experiments like the dual-slit experiment, now with larger and larger objects, entanglement (again, with larger objects), is telling us something. The way to handle it should be to accept what we see as true, not deny the truth. Then do the next step, and eventually we may discover more, and adjust our understanding. Denial won't get us anywhere.
...But we can, as is pretty clear for anyone learning electronics from scratch, at least late enough that semiconductors and transistors...
Wait a minute. We don't need no new fangled transistors. Back in the day we demonstrated the existence of single photons with tubes, photo-multiplier tubes.
All of which is the photo-electric effect, from which we can infer photons, as described by Einstein in 1905.
Oddly enough the guy who started all this energy quantization business, Max Planck, did not accept the photon-idea.
It was not till later with Compton's scattering experiments that the idea of photons became inescapable.
Oddly enough the guy who started all this energy quantization business, Max Planck, did not accept the photon-idea.
And Einstein, who used Planck's work to describe what Planck didn't believe in, went on to be the first to describe quantum entanglement, originally as a disproof. . but he never believed in non-locality. Einstein contributed massively to quantum mechanics. But did not believe in all of the consequences. And black holes came out of Einsteins equations, which he also found troubling. And so it goes. This just goes to show that it's better to believe the truth of what experiments and equations say, instead of rejecting it based on philosophical issues.
The more I find out Einstein about astounding it all is.
He starts out with some intuition about how things are. For example, there is no difference between gravity and acceleration. The Einstein equivalence principle.
Then spends ages developing the mathematical models based on that intuition. A long time in the case of general relativity. Lo it works!
But then the very mathematical model he creates leads to predictions of things he really does not like. His intuition won't allow him to go there any more. Black holes is one example. The cosmological constant is another.
He did not like the randomness of Quantum Mechanics, "God does not play dice...." etc. But QM starts with Einstein's model for the photoelectric effect. Among other things.
Speaking of which I find all of Physics weird, going back to Newton.
Newton came up with his laws of gravitation and motion. From which grows the whole world of Newtonian mechanics. The deterministic clockwork universe.
However he offered no explanation as to what gravity actually was. As Newton said "I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses;"
But the thing is Newtons model of gravity relied on an instantaneous "spook" action at a distance. A concept that troubled many. But that "trouble" got brushed aside over the years until Newtons model became the "reality" in the minds of Physicists. They stopped worrying about it.
Now similarly, when Newtonian mechanics started to creak under the strain of new observations, Quantum Mechanics arrived on the scene. QM describes things beautifully and to great accuracy. QM lead to predictions that worked out, Lasers, Transistors etc.
But at the heat of QM we have a weirdness, the built in and unexplained randomness of events. That weirdness troubled many. Like Einstein.
Again after a 100 years of QM that weirdness seems to have been brushed aside. Seems young'ns today just accept it, or perhaps never get encouraged to think about it. Like that weird instantaneous action at a distance of Newtons.
Comments
On the one hand we have experiments that demonstrate the photon nature of light. You can count them one by one as you might expect for some kind of indivisible particle.
On the other hand, even if you are working with one photon at a time the place where it ends up, statistically after many experiments, is described by the notion of waves.
How can one particle-like thing explore the space of all options like a wave and end up where it does in a particle like manner?
I urge you to do the experiments.
Now, I do agree with you. Perhaps our notion of particles is wrong. Perhaps our notion of waves is wrong. Perhaps the mathematical models built from these notions is wrong.
When I say "wrong" I don't mean the mathematical models don't work to some extent but rather they are not capturing some essence of what is going on underneath.
That is what physics is all about, perfecting the notions, and hence the mathematical models.
Newton is famous for giving us his laws of gravitation. He also said "I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses". That is to say, the maths works but I have no idea why.
Feynman has said much the same.
Bottom line is, it's easy to poke fun at physics, but it's hard to come up with some useful ideas that work better.
Dualism is at large a method to show people that you are smarter. Since ever there is a discussion about atoms and continua. The perspective changed over the millenia. Now we know, yes, there is a continuum, but this continuum can be separated into local areas, which then are particles. But that doesn't mean, that there is a wave or a particle, it just means that there is a way to have located standing waves. Whatever a standing wave looks like. A wave caught between two mirrors is a very simple example. A wave caught in the atom is much more complicated, but follows the same concept.
By the way: Feynman wrote a lot, as every scientist writes a lot over his lifetime, only a few is narrated. Feynman showed: if we have a wave and in the running path of this wave are gratings, then the interference pattern of the wave encodes the structure of the grating. And he showed, that when the grating is of infinity density, then the interference pattern is that of a free running wave. Therefor he said: let us asume, the free space is an grating such dense, that we can not proof the existence. But now we can calculate the movement of wavelets and calculate all the possible pathes and in the end we see that the shortes path is nothing but the interference of all thinkable pathes. This is just a mathematical approach. Now, that you have this dense grating you can introduce disturbances and calculate what happens now. The same mechanism works if you try to understand semiconductors and doping
It makes a certain amount of sense that if one has two oscillator operating at two different frequencies with the same quantum efficiency, then during a certain period, the number of photons is going to be proportional to the frequency... giving a rational explanation for this relation.
But if I understand what Erna is saying(and which I have believed for a while might actually be the case): In the case of single photons... (the instantaneous case) the momentum of all photons is the same and therefore a quantum of action is defined and can be assigned a value of 1.
Actual values of Pi must be discreet. There is no need for a number which cannot be expressed.
Both these quantities are conserved. So two colliding objects may have different energies after they collide than they had before but the sum of their energies is the same. Similarly for the sum of their momenta.
So what about light?
We observe that light comes in lumps. We can see this by playing with photo-multiplier tubes, basically the photo-electric effect described by Einstein. These lumps of light, photons, carry energy. Obviously, else the sun would not warm us and photo cells would not work. They also, less obvious perhaps, carry momentum.
Energy E = h * f and momentum p = h / λ.
In short, the "when is momentum..." true when we have a photon in flight. Which is pretty much whenever we have a photon at all.
What about that conservation?
Hmm... Crash particles together and they may break up or combine to give different particles and photons flying out as wreckage. All those resulting bits will have the same total energy and momenta as the original particles. To account for that we use the above formulae.
I can't make out what that is trying to say. Consider a laser, that is a resonant cavity, an oscillator. The number of photons it puts out can be increased by driving it harder, turn up the current, you get more photons hence energy out. But they all have the same frequency and each has carries the same energy.
I can't make out what that is tryinng to say either. The momentum of a photon depends on it's wavelength, see above, they are not all the same. Unless you are talking of all photons of the same frequency.
Sure we could define Planck'c constant as 1. We would then have to redefine all our other units, length, time, etc to match. I'm not sure what advantage that has.
Now, where all this gets confusing is when we observe in experiment that we can get interference effects with particles like electrons, protons, even entire atoms and molecules. These interference effects look much the same as we see for light or sound or ripples in water. We can describe them using the mathematics of waves. So we are forced to the conclusion that particles have a wave like nature.
This recent experiment observes wave interference patterns created by streaming Bucky Balls (C60) though a diffraction grating. https://www.univie.ac.at/qfp/research/matterwave/c60/ I mean wow! A Bucky Ball is a huge molecule made of 60 carbon atoms. And there it is moving according quantum mechanical wave equations.
I'm not sure what you mean by "discreet" here. There is only one actual value of Pi. It's the ratio of a circles circumference to it's diameter. Sure we use approximations.
Not sure what you mean by "cannot be expressed" either. Sure we cannot write down the exact numerical value but it is expressed as C/D. We use numbers that "cannot be expressed" all the time, e, i, the square root of two etc.
I just ripped a shaft encoder wheel out of an old Cannon printer. If I squint really hard at it under good light I can just about make out the black stripes printed on the transparent wheel. I have no idea how many stripes per revolution that is.
Anyway, shining a red laser pointer through those stripes gives me a nice diffraction pattern on the wall. Which kind of surprises me as I thought we needed a much finer grating to do that. I have not done the maths on this yet.
Next step would be to turn the brightness down until we can count one photon at a time with a photo-multiplier tube or solid state photon counter. Scanning the image plane with the photon counter we should be able to plot the diffraction pattern.
I'd really like to do this because having read about it a lot and done the diffraction thing with lasers and x-rays I have never actually done the one photon at a time thing.
Where it gets weird of course is that this diffraction phenomena happens even with things we would normally say are solid particles, like electrons or whole molecules, that we would normally say cannot pass through many parts of a diffraction grating at the same time. But if one particle only passes through one slot in the grating how can there be an interference pattern?
Now one might say there are no particles only waves. But that leaves a lot of things unexplainable. Or say there are no waves only particles, again a lot of things, like interference, are unexplainable.
Or one might say we are just looking at it wrong, there is no particle and no wave, it's something else. Fine, what is the idea? Shows us the maths?
The idea of radiation consists of photon is not needed to understand the dualism of light waves: whenever a photon is absorbed, there is matter in play. And if matter can change state only in quanta, it is clear, that you will only see light quantums. But it is not the light, that is quantized, it's your measuring instrument that takes a quantum of energy from the field and stores it in a place.
How to understand the double slit experiment? Your target consists of molecules that when absorbing energy from the field, are "blackend". If now the field, that fills the vacuum, is carrying very low levels of waves of a given frequency, then the wave travelling through the slits interferes "constructively" and in the plane of the detector molecule by accident the constructed wave amplitude is sufficient to excite a molecule. A quantum of energy at the resonance frequency of the molecule is transfered from the field to the matter. That is what you call a photon.
That is: a photon is not a particle, light is made of, but it is the event of transfer from energy and momentum between field and matter. More we can not know, because we can not see the field itself, only interaction. That is why I say: hocus pocus. We need no quantized radiation to understand why energy exists in quanta.
Planck for example was very explicit in this. He said: in the walls of a hollow block body are oscillators and they quantize radiation. And he said: the spectrum we measure is independent of the frequency of the oscillators, if only the fundamental energy is low.
Einstein/Bose found: it is not the wall, that carrying the hypothetical oscillators, it is the space itself! If the walls are mirroring the radiation, that standing waves have a fundamental frequency and all harmonics. And if statistics is applied to calculate the ensembles of possible energy distributions, then the result is the black body radiation.
So the math doesn't change. It is only: there is a wave field, quantized by measuring it.
But to me there are other open questions: We know the term wave resistance, that is an "imaginated" resistance when a free wave exists and electric and magnetic field strength are related. (we also imagine a resistance, if we measure current and voltage, no need to understand the "mechanics" of the resistor.) So: when the big bang happend, and radiation started to travel away, is there a wave resistance where no wave ever travelled? We know, that a travelling wave, when arriving at different wave resistance is partly reflected. So if there is no wave resistance when there is no wave, will the wave front be partly reflected and so the expansion slow down?
That shows: if we overcome the hocus pocus, a lot of questions worth to discuss remain.
It's like the time when I was 9 years old that my father happen to mention that nothing can travel faster than the speed of light. That made no sense to me. That's just a speed like any other, you can always go faster. My father was obviously wrong. Took a long while to start to understand why his statement had to be true.
Anyway, down to business: So riddle me this:
1) I have a transmitter of light. Say a hydrogen atom with an electron in an excited state ready to drop down and emit light.
2) I have two receivers of light. Say photographic plates that register black dots when exposed.
3) I put my receivers far away from the transmitter in opposite directions.
4) My transmitter launches some light. That excited electron gives up it's "quanta" of energy.
5) That light travels in all directions, as you claim it's a wave, that's what a wave does. Therefore half the energy of our quanta goes towards one detector and half in the opposite direction to the other.
6) Now there is not enough energy going in either direction to register on any detector, There isn't enough to make up the "quanta" the detector requires.
7) Therefore my light energy can never be detected. It's floating around in space forever. Lost.
8 ) But it is! Either to one side or the other.
Are we to assume the emitted wave travels all the way to both detectors, say A and B, then somehow a decision is made that the "quanta" of of energy should be absorbed by one of them, say A? Which implies that the half of the energy that travelled to B now has to instantly move to A to complete the process. That can't be, it requires light to travel faster than light!
Or are we to assume that energy always stayed bound up in a particle like packet, a photon, that goes from emitter to detector in a lump. And causes the observed phenomena? That sounds more like it.
End of riddle.
Of course that photon lump of energy idea then presents a further puzzle. On the one hand our wave notions of light suggest that half of something went left to detector A and half went right to detector B. On the other hand our photon lump notion, that we are forced to accept by experiment as above, suggests the energy travelled in only one direction to A or B.
This brings us to the fundamental quantum mechanical wave/particle duality issue that has given me headache since 1976 and puzzled many far greater minds since a hundred years or so. Physicists still cannot agree among themselves on a single interpretation of all this.
If you think about it, the thought experiment above is equivalent to the slits experiment. Without the complication of interference.
I think the problem is that the idea of actual photons is required to explain experimental results. Which is much better explained by others:
http://scienceblogs.com/principles/2010/08/05/whats-a-photon-and-how-do-we-k/
Any way, this thread has been sunk. So there is not much point in continuing this fascinating debate here.
Being a physicist or not: a single object being in two places in one moment is a contradiction in itself and that is the only reason, why a different solution must exist. Because this experiment exists and show the intereference and quantized behavior (particles).
But what is so strange in: if the propability of detecting a single photon is 1%, then 100 photons look like one? In this case, 50 photons can pass each slot and in this case the "detected" photon is the interference of both photon beams.
This is a Gedankenexperiment, it can not be realized, because the concept of single photons is academic and to measure energy/wavelength you need more precision than the Heisenberg Uncertainty relation allows
When we do experiments with light, say the Young's slits experiment, we come to the conclusion that light is a wave phenomena. The mathematics of waves gives us the resulting interference patterns. Certainly Maxwell's equations deal with a wave phenomena and seem to fit the observations very well.
Other experiments, involving the photoelectric effect, or just doing that Young's slits experiment at very low light levels, lead us to the conclusion we are dealing with particles, aka photons. We can hear the single click of a photon counter, we can see the single dot exposed on a photographic plate.
The Young's slits experiment at very low light levels gives us a problem because now we observe both wave like and particle like behaviour in the same experiment. WTF?
It get's worse....
I can start with a lump of stuff. Say carbon. We can break it down to ever smaller and smaller parts. Ending up with C60 molecules for example, Bucky balls. At that point we have surely have "particles".
BUT, wait, we can now do the Young's slits experiment with a beam of those C60 particles and observe interference effects just like we see when we do the experiment with light "waves".
Holy cow, now we have to accept that our beam of solid particles is behaving like a beam of light waves.
Which of course is the stuff of Qunatum Mechanics.
All this leads me to the following conclusion:
If you insist that single photons do not exist then you are insisting that C60 molecules don't exist.
Now, I assume that what you really mean is that we can't send one photon at a time. But we can, as is pretty clear for anyone learning electronics from scratch, at least late enough that semiconductors and transistors were on the curriculum. Transistors can't work unless quantum mechanics works exactly as described, and part of it is that if one electron drops from its shell to a lower shell, you get one (1) photon output. In any case, there are also real devices created for single photon output, so if you don't believe in single photons then you must also believe this device is a hoax: http://www.physique.ens-cachan.fr/old/franges_photon/single_photon_source.htm
And of course, the experiment has now been done with much bigger objects than photons, e.g. Heater's buckyballs.
You refer to how physical objects should behave according to intuition. But what is physical reality? Most of you, or as close to all of you as you can imagine, consists of nothing. When you press your hand on a table and feel resistance, what you feel is the force of electrons, it's not something physical, not really. Your weight, that is, the weight of your protons, are 92% or so due to relativistic effects (mass increases as speed increases) of the insane speeds of the quarks your protons are made of. What are electrons made of?
The problem with physical objects and reality is, I believe, that we don't actually understand, yet, what it is. And what we observe with experiments like the dual-slit experiment, now with larger and larger objects, entanglement (again, with larger objects), is telling us something. The way to handle it should be to accept what we see as true, not deny the truth. Then do the next step, and eventually we may discover more, and adjust our understanding. Denial won't get us anywhere.
All of which is the photo-electric effect, from which we can infer photons, as described by Einstein in 1905.
Oddly enough the guy who started all this energy quantization business, Max Planck, did not accept the photon-idea.
It was not till later with Compton's scattering experiments that the idea of photons became inescapable.
That's right.
The more I find out Einstein about astounding it all is.
He starts out with some intuition about how things are. For example, there is no difference between gravity and acceleration. The Einstein equivalence principle.
Then spends ages developing the mathematical models based on that intuition. A long time in the case of general relativity. Lo it works!
But then the very mathematical model he creates leads to predictions of things he really does not like. His intuition won't allow him to go there any more. Black holes is one example. The cosmological constant is another.
He did not like the randomness of Quantum Mechanics, "God does not play dice...." etc. But QM starts with Einstein's model for the photoelectric effect. Among other things.
Newton came up with his laws of gravitation and motion. From which grows the whole world of Newtonian mechanics. The deterministic clockwork universe.
However he offered no explanation as to what gravity actually was. As Newton said "I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses;"
But the thing is Newtons model of gravity relied on an instantaneous "spook" action at a distance. A concept that troubled many. But that "trouble" got brushed aside over the years until Newtons model became the "reality" in the minds of Physicists. They stopped worrying about it.
Now similarly, when Newtonian mechanics started to creak under the strain of new observations, Quantum Mechanics arrived on the scene. QM describes things beautifully and to great accuracy. QM lead to predictions that worked out, Lasers, Transistors etc.
But at the heat of QM we have a weirdness, the built in and unexplained randomness of events. That weirdness troubled many. Like Einstein.
Again after a 100 years of QM that weirdness seems to have been brushed aside. Seems young'ns today just accept it, or perhaps never get encouraged to think about it. Like that weird instantaneous action at a distance of Newtons.